Linear active two-port network for expanding or compressing characteristic curve of two-terminal device

ABSTRACT

A linear active two-port network element for synthesizing nonlinear network components with arbitrarily prescribed characteristics. The elements, by themselves or in combination, can be utilized for a variety of applications, and are particularly useful in integrated circuit technology. The element included herein is the Scalor. The Scalor expands or compresses the characteristic curve of any two-terminal device along a predetermined axis or axes without altering the shape of the curve.

United States Patent Inventor Appl. No.

Filed Patented Assignee Leon 0. Chua West Lafayette, 1nd. 732,185

May 27, 1968 Nov. 9, 1971 Purdue Research Foundation LINEAR ACTIVE TWO-PORT NETWORK FOR EXPANDING OR COMPRESSING CHARACTERISTIC CURVE 0F TWO-TERMINAL DEVICE 12 Claims, 15 Drawing Figs.

U.S. Cl 307/230, 307/317, 333/80 T Int. Cl G06g 7/12 Field of Search 333/24, 80,

80 T, 14, 20; 330/30 D, 38 Ml; 328/14, 142;

[5 6] References Cited UNITED STATES PATENTS 3,289,107 11/1966 Zellmer et al Primary ExaminerEli Lieberman Assistant Examiner-Paul L. Gensler Attorney-John R. Nesbitt ABSTRACT: A linear active two-port network element for synthesizing nonlinear network components with arbitrarily prescribed characteristics. The elements, by themselves or in combination, can be utilized for a variety of applications, and are particularly useful in integrated circuit technology. The element included herein is the Scalor. The Scalor expands or compresses the characteristic curve of any two-terminal device along a predetermined axis or axes without altering the shape of the curve.

CHARACTERIZATION AND REALIZATION OF SCALORS TYPE SYMBOL AND CHARACTERIZATION TRANSMISSION MATRIX I I I I I3] BASIC REALIZATIONS USING CONTROLLED SOURCES VOLTAGE SCALOR (V- SCALOR) CURRENT SCALOR POWER SCALOR (P- SCALORI REALIZATION l REALIZATION 2 l 2 2 1 0- -o+ o w- REALIZATION a REALIZATION4 1 2 i 2 REALIZATION I V v @K -III 2 REALIZATION 2 REALIZATION 3 REALIZATIONZ REALIZATION 4 REALIZATION I i2 '1 2 REALIZATION3 REALlZATION 4 i l2 I PAIENTEDuuv 9 1971 sum 2 OF 3 FIQQ Z (a) PRACTICAL REALIZATION OF A VOLTAGE SCALOR 2 lson FIG, ,3 (b) PRACTICAL REALIZATION OF A CURRENT SCALOR INVENTUR. LEON O. CHUA ATTORNEY PAIENIEDIIUII 9 IQII 3,619 6S0 SHEET 3 [IF 3 1-V cURvE OF I-V CURvE OF RESULTING I-V CURvE OF RESULTING 1-v CURvE OF' RESULTING NONLINEAR RESISTOR RESISTOR wITH THE RESISTOR wITH THE RESISTOR WITH BOTH vOLTAGE EQUAL TO TwICE CURRENT EQUAL TO TwICE vOLTAGE ANO CURRENT FIG 4 THE ORIGINAL vALUE THE ORIGINAL vALUE EQUAL TO TwICE THE (K =2) (K =2) ORIGINAL vALUL FIG-.5 I q 6 (K =2,K =2) vERTICAL SCALE: I 2m PER DIVISION HORIZONTAL SCALE: v= 2.5 vOLTs PER DIVISION FIG. 7

(0). SCOPE TRACINGS DEMONSTRATING THE SCALING OF THE I-V CURVE OF A NONLINEAR RESISTOR BYA V-SCALOR, AN I-SCALOR, S A P-SCALOR @"I CURVE OF 1 I CURVE OF RESULTING I CURVE OF RESULTING @I CURVE OF RESULTING NONLINEAR INOUCTOR INDUCTOR WITH THE INDUCTOR WITH THE INDUCTOR WITH BOTH CURRENT EQUAL TO TWICE FLUXLINKAGE EQUAL TO CURRENT a FLUX'LINKAGE 8 THE ORIGINAL VALUE TWICE THE ORIGINAL EQUAL TO TWICE THE (K =2) VALUE (K =2) ORIGINAL VALUE F] I 2, K 2) VERTICAL SCALE 4b I MICROWEBER-TURN PER DIVISION HORIZONTAL SCALE: I ImG PER DIVISION (b). SCOPE TRACINGS DEMONSTRATING THE SCALING OF THE -I CURVE OF A NONLINEAR INDUCTOR BY AN I-SCALOR, A V-SCALOR, G A P-SCALOR vI fI vIvI Q-v CURvE OF Q=V CURvE OF RESULTING Q-v CURVE OF RESULTING Q-v CURvE OF RESULTING NONLINEAR CAPACITOR CAPACITOR wITH THE CAPACITOR wITH THE CAPACITOR wITH BOTH vOLTAGE EQUAL TO TwICE CHARGE EQUAL To TwICE vOLTAGE a CHARGE THE ORIGINAL vALUE THE ORIGINAL vALUE EQUAL To TwICE THE IK =2) (K =2) THE ORIGINAL vALUE v Fm- 15 1 (K =2, K =2) VERTICAL SCALE Q=| MICROCOULOMB PER DIVISION HORIZONTAL SCALE V =I VOLT PER DIVISION (c). SCOPE TRACINGS OEMONSTRATING THE SCALING OF THE Q-V CURVE OF A NONLINEAR CAPACITOR BY A V-SCALOR AN I-SCALOR, 8 A P-SCALOR INVI;'N'I'( m.

SCOPE TRACINGs DEMONSTRATING THE SCALING LEON CHUA OF THE I-V, Q-I, OR Q-V CURVE OFA NONLINEAR BY RESISTOR INDUCTOR, OR CAPACITOR BY SCALORS ATTORNEY FIELD OF THE INVENTION This invention relates to an active 2-port network element, and, more particularly, relates to an active 2-port network element and combinations thereof for realizing components with arbitrarily prescribed characteristics.

DESCRIPTION OF THE PRIOR ART A basic problem has existed in the electronics field both in nonavailability of devices or components capable of performing a desired function, and in nonavailability of devices or components which are suitable for a desired function or usage. For example, a basic problem has heretofore existed in realizing a nonlinear resistor, inductor, or capacitor with a prescribed Voltage-Current (V-l), Flux-Linkage-Current (d l), -I), Charge-Voltage (Q-V) curve. In addition, in connection with integrated circuits, many problems have arisen, including, for example, the necessity for practical inductorless circuits. These, and other, unsolvedproblems have. made it necessary to seek new building blocks to enable the realization of components or devices which will exhibit the desired characteristics and yet be suitable for usage in the contemplated manner.

The widespread application of computers in network analysis and optimization problems and the phenomenal progress in integrated circuit technology over the past few years have removed, as well as introduced, many new circuit constraints which have hitherto been regarded as purely academic. In the case of computer applications, for example, it is now possible to specify a set of desired network functions and let the computer select the optimum values of a set of linear resistors, inductors, and capacitors so that the deviations of the resulting networks perfonnance from the desired specification is minimized. However, in view of the limited capability of such linear elements, the resulting optimum linear network may still far from satisfactory because the deviations can still be significant. Under this condition, it is necessary to enlarge the class of allowable network elements to include nonlinear resistors, inductors, and capacitors. Since the class of linear elements is a subset of this larger class, it is clear that the optimized network should be at least as good, if not better,-than the linear case. In other words, given two networks with the same topology, an optimum choiceof nonlinear elements will in general out-perfonn an optimum choice of linear elements. Conversely, given two networks for realizing identical functions (one using nonlinear elements, and the other using only linear elements), the nonlinear version should in general require a smaller number of network elements.

Since the nonlinear elements that exist in their natural form have characteristic curves which are governed by the physical properties of the materials composing the elements, it is to be expected that the I-V, I -1, and Q-V curves as required by an optimum network will not be commercially available. Hence, before one can realize an optimum nonlinear network, it is necessary to synthesize a nonlinear resistor, inductor, or capacitor with a prescribed I-V, ll-I, or Q-V curve, using only commercially available components as building blocks. This fundamental problem is often referred to as the nonlinear element realization problem.

Before the advent of integrated circuits, the nonlinear element realization problem was rather academic because it was difficult to combine many discrete components without introducing an excessive amount of parasitics. Moreover, since active elements are usually required, the amount of power dissipation could be prohibitive. Even if these difficulties can be circumvented, the physical size of the synthesized element would be too bulky. These practical considerations can now be overcome by using integrated circuits. It is no longer unrealistic to think of a nonlinear element made up of a few dozen resistors, zener diodes and transistors because the finished size of the integrated circuit need not be larger than the present discrete components. Hence, the parallel development of computer optimization techniques and integrated circuit technology has rendered the nonlinear element realization problem a rather pressing one.

SUMMARY OF THE INVENTION This invention provides a solution to many of the problems now existing in the electronics field through the introduction of linear active 2-port network elements and combinations thereof heretofore unknown. Through the use of these network elements prescribed, nonlinear components can be realized that were heretofore unobtainable.

It is therefore an object of this invention to provide linear active 2-port network elements and combinations thereof not heretofore available.

It is still another object of this invention to provide a scalor for expanding or compressing the characteristic curve of any 2-tenninal device along a predetermined axis or axes without altering the shape of the curve.

With these and other objects in view which will become apparent to one skilled in the art as the description proceeds, this invention resides in a novel construction combination and arrangements of parts substantially as hereinafter described and more particularly defined by the appended claims, it being understood that such changes in the precise embodiments of the herein disclosed invention may be included as come within the scope of the claims.

FIG. 1 (A), (B), and (C) is a table showing scalor characterization and realization.

FIG. 2 is a circuit diagram of a voltage scalor.

FIG. 3 is a circuit diagram of a current scalor.

F IGS. 4 through 7 are graphical illustrations showing scaling of the IV curve of a nonlinear resistor by a V-scalor, an I- scalor, and a-P-scalor, and wherein FIG. 4 is the l-V curve of the nonlinear resistor, FIG. 5 is the l-V curve of the resulting resistor with the voltage equal to twice the original value, FIG. 6 is the I-V curve of the resulting resistor with the current equal to twice the original value, and FIG. 7 is the I-V curve of the resulting resistor with both voltage and current equal to twice the original value.

FIGS. 8 through 11 are graphical illustrations showing scaling of the I I curve of a nonlinear inductor an l-scalor, a V- scalor, and a P-scalor, and wherein FIG. 8 is the l -l curve of a nonlinearinductor, FIG. 9 is the 1H curve of the resulting inductor with the current equal to twice the original value, FIG. 10 is the D-I curve of the resulting inductor with the flux-linkage equal to twice the original value, and FIG. 11 is the d -l curve of the resulting inductor with both current and flux-linkage equal to twice the original value.

FIGS. 12 through 15 are graphic illustrations showing scaling of the Q-V curve of a nonlinear capacitor by a V-scalor, an I-scalor, and a P-scalor and wherein FIG. 12 is the Q-V curve of a nonlinear capacitor, FIG. 13 is the Q-V curve of the resulting capacitor with the voltage equal to twice the original value, F IO. 14 is the Q-V curve of the resulting capacitor with the charge equal to twice the original value, and FIG. 15 is the Q-V curve of the resulting capacitor with both voltage and charge equal to twice the original value.

The current, voltage, or power rating of most solid state or electron devices is usually restricted by some physical property of materials. For example, due to the tunneling mechanism, a tunnel diode is inherently a low-voltage device. It would therefore be also useful to find a practical method to scale the current, voltage, or power of a device to any prescribed range of values. This an be accomplished with a 2-port network element described hereinafter and referred to as a scalor. There are three types of scalors-a voltage scalor, a current scalor, and a power scalor. The symbols and transmission matrices for these three elements are given in FIG. I. It can be easily shown that a voltage scalor also scales the flux-linkage and a current scalor also scales the charge. Hence, scalors can also be used to scale the (D-l curve of an inductor or the Q-V curve of a capacitor.

A voltage, current, or power scalor can be realized by either one or two controlled sources. Several basic realization schemes for each type of scalor are shown in FIG. 1. Observe that the cascade connection of a voltage scalor with a current scalor results in a power scalor. Two practical circuits for realizing voltage or current scalors are shown in FIGS. 2 and 3.

The circuit shown in FIG. 2 simulates the Realization l" for the voltage scalor in FIG. I. The NEXUSSQ-la represents an operational amplifier manufactured by the NEXUS Company. This operational amplifier is used to sense the voltage v to produce a voltage v =(K 1v,. Hence the operational amplifier circuit is used to simulate the voltage controlled voltage source (the diamond-shape symbol) required by Realization l. The scaling constant K, of this voltage scalor circuit is varied by adjusting the 5.-KQ poten- ,tiometer connected between the emitter of the transistors and lO-K-Q. resistor. This potentiometer controls the voltage gain of the operational amplifier circuit.

The circuit shown in FIG. 3 simulates the Realization l" for the current scalor in FIG. I. The two-transistor circuit is used to simulate current-controlled current source (diamondshape symbol) required by Realization l. The scaling constant K, of this current scalor is varied adjusting the l-K-O. potentiometer. This potentiometer controls the current gain of the transistor current amplifier circuit.

Several scalor circuits have been designed and built, and to demonstrate the effect of the scalor on the I-V curve of a nonlinear resistor, graphs representing scope tracings are shown in FIGS. 4, 5, 6 and 7. These tracings represent a scaling operation on voltage (FIG. 5), current (FIG. 6), and power (FIG. 7). In order to demonstrate the scaling operation on the I -I curve of an inductor, a suitable sample is chosen and obtained by connecting a nonlinear resistor across port 2 of an L-R Mutator which is disclosed in applicants Ser. No. 732,403. The resulting i -I curve and their scaled versions are shown in FIGS. 8, 9, l0, and 11. Similarly, a nonlinear resistor is connected across a C-R Mutator, also disclosed in application Ser. No. 732,403, referred to above, to obtain a good Q-V curve sample. The resulting scaling operations are shown by the scope tracings in FIGS. 12, 13, 14 and 15.

A scalor is by definition an infinite bandwidth element. However, the frequency characteristics of practical scalors are restricted by the frequency characteristics the active elements inside the scalor.

I claim:

I. A linear active 2-port voltage scalor circuit comprising a single voltage-controlled voltage source connected between port I and port 2 with terminal voltage equal to v=(k,v where K, is the voltage scaling constant, and v is the voltage across port 2, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the voltage axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve 2. A linear active 2-port voltage scalor circuit comprising a single voltage-controlled voltage source connectedlbetween port I and port 2 with terminal voltage equal to v=(f 1 v where K, is the voltage scaling constant, and v, is the voltage across port 1. forming a 2-port network such that the charac teristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the voltage axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

3. A linear active 2-port voltage scalor circuit comprising a voltage-controlled voltage source across port 1 with terminal voltage equal to v=K, v and a current-controlled current source across port 2 with terminal current equal to i=1], where K, is the voltage scaling constant 1', and v, are the current and voltage at port 1 and port 2 respectively, forming a Z-port netacross port 2 with terminal voltage equal to win, where K,

is the voltage scaling constant, v, and i are the voltage and current at port 1 and port 2 respectively, forming a 2-port network such that the characteristics curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the voltage axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

5. A linear active Z-port current scalor circuit comprising a single current-controlled current source connected between port 1 and port 2 with terminal current equal to r(K,l) i,, where K, is the current scaling constant, and i is the current entering port 2, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

6. A linear active 2-port current scalor circuit comprising a single current-controlled current source connected between port I and port 2 with terminal current equal to i=(fG-I )1},

where K, is the current scaling constant, and i, is the current entering port I, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

7. A linear active 2-port current scalor circuit comprising a current-controlled current source across port 1 with terminal current equal to 'FK i and a voltage-controlled voltage source across port 2 with terminal voltage equal to v==v where K, is the current scaling constant, v, and i, are the voltage and current at port I and port 2, respectively, forming a 2- port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

8. A linear active 2-port current scalor circuit comprising a voltage-controlled voltage source across port I with terminal voltage equal to v=v,, and a current-controlled current source across port 2 with terminal current equal to Fm where K, is

the current scaling constant, i I and v, are the current and voltage at port I and port 2 respectively, fonning a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

9 A linear active 2-port power scalor circuit comprising a voltage-controlled voltage source across port I with terminal voltage equal to v=K, v and a current-controlled current 1 source across port 2 with terminal current equal to (=75 I l source across port 2 with terminal voltage equal to v=f v where K, and K, are the current and voltage scaling constants, and where v, and i: are the voltage and current port 1 and port 2 respectively, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along both the voltage axis, and the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

11 A linear active 2-port power scalor circuit comprising a cascade connection between a 2-port voltage scalor having a voltage scaling constant equal to K, one of the ports of said voltage scalor forming port 1 of said power scalor and a 2-port current scalor having a current scaling constant equal to K one of the ports of said current scalor being connected to the other of the ports of said Z-port voltage scalor and the other port of said 2-port current scalor forming port 2 of said power scalor, such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along both the voltage axis and the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.

12, A linear active 2-p0rt power scalor circuit comprising a cascade connection between a 2-port current scalor having a rent scalor forming port 1 of said power scalor, and a voltage scalor having a voltage scaling constant equal to K,, one of the ports of said voltage scalor being connected to the other of the ports of said 2-port current scalor and the other port of said 2 port voltage scalor forming port 2 of said power scalor, such that the characteristic curve of a given nonlinear circuit com- 

1. A linear active 2-port voltage scalor circuit comprising a single voltage-controlled voltage source connected between port 1 and port 2 with terminal voltage equal to v (kv-1)v2 where Kv is the voltage scaling constant, and v2 is the voltage across port 2, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the voltage axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 2. A linear active 2-port voltage scalor circuit comprising a single voltage-controlled voltage source connected between port 1 and port 2 with terminal voltage equal to v ( -1) v1, where Kv is the voltage scaling constant, and v1 is the voltage across port 1, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the voltage axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 3. A linear active 2-port voltage scalor circuit comprising a voltage-controlled voltage source across port 1 with terminal voltage equal to v Kv v2, and a current-controlled current source across port 2 with terminal current equal to i i1, where Kv is the voltage scaling constant, i1 and v2 are the current and voltage at port 1 and port 2 respectively, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the voltage axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 4. A linear active 2-port voltage scalor circuit comprising a current-controlled current source across port 1 with terminal current equal to i i2, and a voltage-controlled voltage source across port 2 with terminal voltage equal to v v1, where Kv is the voltage scaling constant, v1 and i2 are the voltage and current at port 1 and port 2 respectively, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the voltage axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 5. A linear active 2-port current scalor circuit comprising a single current-controlled current source connected between port 1 and port 2 with terminal current equal to i (KI-1) i2, where KI is the current scaling constant, and i2 is the current entering port 2, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 6. A linear active 2-port current scalor circuit comprising a single current-controlled current source connected between port 1 and port 2 with terminal current equal to i ( -1)i1, where KI is the current scaling constant, and il is the current entering port 1, forming a 2-port network such that the characteristic curve of a given nonLinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 7. A linear active 2-port current scalor circuit comprising a current-controlled current source across port 1 with terminal current equal to i KIi2, and a voltage-controlled voltage source across port 2 with terminal voltage equal to v v1, where KI is the current scaling constant, v1 and i2 are the voltage and current at port 1 and port 2, respectively, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 8. A linear active 2-port current scalor circuit comprising a voltage-controlled voltage source across port 1 with terminal voltage equal to v v2, and a current-controlled current source across port 2 with terminal current equal to i i1, where KI is the current scaling constant, i1 and v2 are the current and voltage at port 1 and port 2 respectively, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 9. A linear active 2-port power scalor circuit comprising a voltage-controlled voltage source across port 1 with terminal voltage equal to v Kv v2, and a current-controlled current source across port 2 with terminal current equal to i i1, where Kv and KI are the voltage and current scaling constants, and where i1 and v2 are the current and voltage at port 1 and port 2 respectively, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along both the voltage axis and the current axis thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 10. A linear active 2-port power scalor circuit comprising a current-controlled current source across port 1 with terminal current equal to i KI i 2, and a voltage-controlled voltage source across port 2 with terminal voltage equal to v v1, where KI and Kv are the current and voltage scaling constants, and where v1 and i2 are the voltage and current at port 1 and port 2 respectively, forming a 2-port network such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along both the voltage axis, and the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 11. A linear active 2-port power scalor circuit comprising a cascade connection between a 2-port voltage scalor having a voltage scaling constant equal to Kvone of the ports of said voltage scalor forming port 1 of said power scalor and a 2-port current scalor having a current scaling constant equal to KIone of the ports of said current scalor being connected to the other of the ports of said 2-port voltage scalor and the other port of said 2-port current scalor forming port 2 of said power scalor, such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along both the voltage axis and the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve.
 12. A linEar active 2-port power scalor circuit comprising a cascade connection between a 2-port current scalor having a current scaling constant equal to KI, one of the ports of said current scalor forming port 1 of said power scalor, and a voltage scalor having a voltage scaling constant equal to Kv, one of the ports of said voltage scalor being connected to the other of the ports of said 2-port current scalor and the other port of said 2-port voltage scalor forming port 2 of said power scalor, such that the characteristic curve of a given nonlinear circuit component connected across port 2 is uniformly altered along both the voltage axis and the current axis, thereby producing a new nonlinear circuit component with a uniformly altered characteristic curve. 